Mr Little has been critical of the Government's reaction to the Australian law change last December, which meant non-Australians who have incurred a prison sentence of a year of more can be deported.
More than 200 Kiwis are currently held in seven detention centres - including on isolated Christmas Island - and Labour's Corrections spokesman Kelvin Davis is currently in Sydney and will visit Villawood Detention Centre this afternoon, and meet families of those held inside.
Mr Davis told the Herald that he met with a partner of one detainee, who talked of her despair and feelings of hopelessness.
"They see no end in sight, there is no end date put on these incarcerations, and they are just at their wits end."
Mr Davis had applied for access and was hoping he could enter Villawood tomorrow, although he said he was not holding his breath.
He had heard disturbing stories from detainees and their families, including one man who was flown to isolated Christmas Island and had been there for nine months.
"He has witnessed people who have slashed their wrists, another guy who slashed his neck."
Mr Davis said Mr Turnbull's visit was the "start of the bromance" with Mr Key, but he was not confident enough pressure would be put on to result in a policy change.
Mr Key will ask Mr Turnbull for the threshold at which a person is deported to be lowered in recognition of the special transtasman relationship, and said this week that he will point out how much New Zealanders living in Australia contributed.
"As a group we are more employed as Australians as a group, we earn more than average Australians as a group, we are actually incarcerated at a lower rate than Australians as a group. New Zealanders are lifters in Australia, they are not leaners."
Mr Turnbull choosing New Zealand as his first international visit as Prime Minister showed that he valued the relationship, Mr Key said.
"It's a relationship that spans everything from our time on the battlefields of places like at Gallipoli, right through to economic integration between the two countries.
"Kevin Rudd in the entire time he was Prime Minister never came to New Zealand. I think the fact he is coming and he is coming here at a time where he knows there are some issues of concern to New Zealand shows that he takes the relationship very seriously."
Mr Turnbull became Australia's prime minister after successfully challenging the leadership of Tony Abbott last month.
Any agreement to alter the immigration policy would be unpopular with some Australian voters and conservative members of Mr Turnbull's own party, and Mr Key has said it is important not to "badger" Australia on the issue, and praised Mr Turnbull as "sensitive".
The Australian Labor Party supported the policy change when it was introduced last year.
Green parties on both sides of the Tasman have called for it to be scrapped and the detentions stopped, and today announced they would be lodging a complaint with the Australian Human Rights Commission about the detention of Kiwis.
"This is a real test for Malcolm Turnbull and he will have some serious questions asked of him when he lands in New Zealand today. Will he let the vestiges of the Abbott government's overreach on immigration law hurt our regional partnerships or will he see sense and let the courts consider these matters on a case by case basis?" said New Zealand Green Party human rights spokesperson Catherine Delahunty.
"There is serious potential for human rights abuses under these new laws. I hope that the Anzac spirit isn't jeopardised by the rashness of the Coalition government's obsession with political point scoring on immigration."
